Vector potential

In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a scalar potential, which is a scalar field whose negative gradient is a given vector field.

Related Topics:
Vector calculus - Vector field - Curl - Scalar potential - Gradient

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Formally, given a vector field v, a vector potential is a vector field A such that

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: mathbf{v} = abla imes mathbf{A}.

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If a vector field v admits a vector potential A, then from the equality

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: abla cdot ( abla imes mathbf{A}) = 0

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(divergence of the curl is zero) one obtains

Related Topics:
Divergence - Curl

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: abla cdot mathbf{v} = abla cdot ( abla imes mathbf{A}) = 0,

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which implies that v must be a solenoidal vector field.

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An interesting question is then if any solenoidal vector field admits a vector potential. The answer is affirmative, if the vector potential satisfies certain conditions.

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